Asymptotic behaviour of Castelnuovo-Mumford regularity
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Abstract:
Let $S$ be a polynomial ring over a field. For a graded $S$-module generated in degree at most $P$, the Castelnuovo-Mumford regularity of each of (i) its $n^{\operatorname {th}}$ symmetric power, (ii) its $n^{\operatorname {th}}$ torsion-free symmetric power and (iii) the integral closure of its $n^{\operatorname {th}}$ torsion-free symmetric power is bounded above by a linear function in $n$ with leading coefficient at most $P$. For a graded ideal $I$ of $S$, the regularity of $I^{n}$ is given by a linear function of $n$ for all sufficiently large $n$. The leading coefficient of this function is identified.References
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Additional Information
- Vijay Kodiyalam
- Affiliation: The Institute of Mathematical Sciences, Chennai, India 600113
- MR Author ID: 321352
- Email: vijay@imsc.ernet.in
- Received by editor(s): October 28, 1997
- Received by editor(s) in revised form: April 15, 1998
- Published electronically: July 6, 1999
- Communicated by: Wolmer V. Vasconcelos
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 407-411
- MSC (1991): Primary 13D02; Secondary 13D40
- DOI: https://doi.org/10.1090/S0002-9939-99-05020-0
- MathSciNet review: 1621961